Now, on the one hand, there is nothing fundamentally wrong with this, since the Copenhagen interpretation is indeed still the standard interpretation of quantum mechanics among physicists. On the other hand, the Copenhagen interpretation has been questioned by some philosophers and physicists for decades, who favored a deterministic interpretation of quantum phenomena (for example, David Bohm, and more recently, James T. Cushing).
Moreover, some recent oil drop experiments have caused more physicists to question the Copenhagen interpretation of quantum mechanics, since phenomena similar to that observed at the quantum level can also be observed at the macro-level with regards to oil drops guided by pilot waves, and no one is tempted to interpret this as evidence for a probabilistic ontology (or however one wishes to characterize it) for droplets of oil.
However, the videos make the common error of asserting that because the equations of quantum mechanics yield true predictions about the behavior of electrons and other particles, this proves that the Copenhagen interpretation of quantum mechanics is correct. But the critics of Copenhagen do not deny the accuracy of the equations of quantum mechanics. What they deny is the standard philosophical interpretation of quantum mechanics: that sub-atomic particles exist in ontologically probabilistic states until they interact with other particles in such a way that their wave function "collapses".
The failure to make this distinction seems related to the most misleading aspect of the second video, which is on "Schoedinger's Cat". The video correctly introduces the Schroedinger's Cat thought experiment as an attempt by Schroedinger to disprove the Copenhagen interpretation of quantum mechanics; Schroedinger thought it was absurd that a cat could be in a superposition between dead and alive before interacting with an observer causes the cat's state to "collapse" like a wave function into either the dead or the alive categories. According to the video, Schroedinger left the field of quantum mechanics altogether, out of his frustration with the standard interpretation of quantum mechanics.
The video then goes on to argue both that Schroedinger's interpretation must be rejected in order to make sense of the way electrons work--which is false--and then to argue that the world as we know it today, with all of its computers and such, would be impossible if it were not for Schroedinger's thought experiment--which is incoherent.
I suppose one cannot expect too much philosophical clarity from TedEd videos, but at least I hope this little imbroglio proves to physicists such as Steven Hawking and science-y types such as Neil DeGrasse Tyson that philosophy may have some value after all, if only in helping to clear up some of the conceptual confusion introduced by well-meaning physicists.
Lest the following point be obscured by the preceding gripefest: the videos are otherwise well-done and are required viewing for the uninformed quantum-ly curious.